Astronomers developed the idea of the mean, or average, in the 19th century. The word mean can be traced to the French meien, which comes from the Latin medianus, meaning the middle, but the history of average is less clear (Eisenhart, 1971). It likely related to ship taxes that were eventually shared equally amongst investors in the 1400’s. The mean was giant leap forward in how humans interpret data, but many argue that it was a giant leap forward in how we interpret ourselves. In any set of measurements, whether it is human personality traits, emissions from cars, or stars in a galaxy, there are differences between the individuals in the set. That is, there is variation. The mean helps us see past this variation to... well, what exactly do we see? Mathematically it is easily defined as something like the central number calculated by adding up all of the values and dividing by the total number of values. The mean of 2, 1, and 9 is (2+1+9)/3 = 4. The mean was one of the key inventions of the scientific enterprise and the Enlightenment, and it permeates every branch of our lives, to the delight of some and the horror of others.

One of the reasons for fear, especially after Foucault’s assault on the norm, was that this concept acts to standardize a single type of human morphology or behavior as the “best”, at least if the mean is interpreted in this way. And while this interpretation is beyond how I think most scientists would interpret it, historically there has been a strong conflation of the mean, or the average, and what is considered average, or normal, behavior. As feminist and queer theorists have pointed out, this conflation of the mean and what is normal has marginalized outsiders, invalidated different lifestyles, and worked to create depression and anxiety in those who don’t match normal standard. This is works especially powerfully in body images, as Cressida Hays, in her book Self Transformation, points out. It is disturbing that our standards of ideal body proportions were developed by actuarial companies.

But is it so easy for us to make this mistake – to take a mathematical concept and construct an ideal? The Lacanian answer is that there actually are norms within our psychic structures, and this is what gives rise to them in the first place. So the mathematical structures are simply capturing a real phenomenon. According to this way of thinking, things like gender and family relations are fundamental structures that act to organize behaviors, making deviations from these central patterns increasingly rare as the diverge from the most mean behavior. One branch of queer and feminist theory has inverted this relationship, via Foucault, by claiming that it is the measurement that actually creates the concept of the ideal norm. There is good evidence for this within the history of behavioral medicine.

I don’t think the extreme version of either position is easy to justify. I know that I am often arguing for the middle ground, but there is evidence that both approaches capture some truth about reality. Certainly long before the Enlightenment, and even before any trace of the mathematical mean (numerical expressions of it pop up thousands of years ago), our species had evolved common behaviors. Foucault’s point focused more on the control of behavior and said nothing about its evolution or neurological foundation. However, the muddy thinking that originally conflated the concept of a normal, or ideal, human with a mathematical construct is still with us and should be forcefully argued against.